He was the son of Patrick Wilson (architect) and Catherine Peddie. His mother died in 1843 when Robert was only eight. In 1849 he began working with his father at 2 Queen Street.
In February 1871 his father died and he inherited his office and clients and he returned to Edinburgh.
He attended William Jewell College, Liberty, Missouri, and was graduated from Centre College, Danville, Kentucky, in 1853. He studied law.
He was admitted to the bar in 1854 and commenced practice in Seguin, Texas, in 1855. He returned to Missouri in 1858. He moved to Leavenworth, Kansas, in 1860.
He returned to Missouri in 1861.
He served as delegate to the 1888 Democratic National Convention. He served as president of the school board of Platte City, Missouri.
Wilson was elected as a Democrat to the Fifty-first Congress. He was reelected to the Fifty-second Congress and served from December 2, 1889, to March 3, 1893.
He served as chairman of the Committee on Pensions (Fifty-second Congress).
He resumed the practice of his profession in Platte City, Missouri. He died in Kansas City, Missouri, December 21, 1916. He was interred in Marshall Cemetery, Platte City, Missouri.
He was a member of the first Kansas House of Representatives from March to June 4, 1861. He served as member of the Missouri House of Representatives in 1871 and 1872 and served as Speaker of the Missouri House of Representatives both years. He served as member of the Missouri State Senate in 1879 and 1880.
